Bernoulli Wavelet-Based Galerkin Method for the Numerical Solution of Second Order Linear Differential Equations with Variable Coefficients

Abstract

Second order linear differential equations with variable coefficients are significant in the representation of various physical phenomena. This study aims to present a Bernoulli wavelet-based Galerkin method (BWGM) for the numerical resolution of these equations. In this framework, we utilize weight functions characterized as Bernoulli wavelets, which act as the foundational elements for deriving numerical solutions. The results achieved through this method are compared with those obtained from traditional methods and the exact solutions. Several problems are chosen to demonstrate the efficiency and applicability of the proposed approach.